Gap function with point nodes in borocarbide superconductor YNi2B2C

Angle-resolved heat capacity of heavy fermion superconductors

Owing to a strong Coulomb repulsion, heavy electron superconductors mostly have anisotropic gap functions which have nodes for certain directions in the momentum space. Since the nodal structure is closely related to the pairing mechanism, its experimental determination is of primary importance. This article discusses the experimental methods of the gap determination by bulk heat capacity measurements in a rotating magnetic field. The basic idea is based on the fact that the quasiparticle density of states in the vortex state of nodal superconductors is field and direction dependent. We present our recent experimental results of the field-orientation dependence of the heat capacity in heavy fermion superconductors CeTIn5 (T  =  Co, Ir), UPt3, CeCu2Si2, and UBe13 and discuss their gap structures.

Unconventional superconductivity in Y5Rh6Sn18 probed by muon spin relaxation

Conventional superconductors are robust diamagnets that expel magnetic fields through the Meissner effect. It would therefore be unexpected if a superconducting ground state would support spontaneous magnetics fields. Such broken time-reversal symmetry states have been suggested for the high—temperature superconductors, but their identification remains experimentally controversial. We present magnetization, heat capacity, zero field and transverse field muon spin relaxation experiments on the recently discovered caged type superconductor Y₅Rh₆Sn₁₈ ( T_C= 3.0 K). The electronic heat capacity of Y₅Rh₆Sn₁₈ shows a T³ dependence below T_c indicating an anisotropic superconducting gap with a point node. This result is in sharp contrast to that observed in the isostructural Lu₅Rh₆Sn₁₈ which is a strong coupling s—wave superconductor. The temperature dependence of the deduced superfluid in density Y₅Rh₆Sn₁₈ is consistent with a BCS s—wave gap function, while the zero-field muon spin relaxation measurements strongly evidences unconventional superconductivity through a spontaneous appearance of an internal magnetic field below the superconducting transition temperature, signifying that the superconducting state is categorized by the broken time-reversal symmetry.

Vortex lattice studies in CeCoIn5 with H is orthogonal to c

We present small angle neutron scattering studies of the vortex lattice (VL) in CeCoIn5 with magnetic fields applied parallel (H) to the antinodal [100] and nodal [110] directions. For H is parallel to [100], a single VL orientation is observed, while a 90° reorientation transition is found for H is parallel to [110]. For both field orientations and VL configurations we find a distorted hexagonal VL with an anisotropy, Γ=2.0±0.05. The VL form factor shows strong Pauli paramagnetic effects similar to what have previously been reported for H is parallel to [001]. At high fields, above which the upper critical field (H(c2)) becomes a first-order transition, an increased disordering of the VL is observed.

Unconventional superconductivity in YNi(2)B(2)C

We use the semiclassical (Doppler shift) approximation to calculate magnetic field angle-dependent density of states and thermal conductivity κ(zz) for a superconductor with a quasi-two-dimensional Fermi surface and line nodes along k(x) = 0 and k(y) = 0. The results are shown to be in good quantitative agreement with experimental results obtained for YNi(2)B(2)C (Izawa K et al 2002 Phys. Rev. Lett. 89 137006).

Unconventional London penetration depth in single-crystal Ba(Fe0.93Co0.07)2As2 superconductors

The London penetration depth lambda(T) has been measured in single crystals of Ba(Fe0.93Co0.07)2As2. The observed low-temperature variation of lambda(T) follows a power law, Deltalambda(T) approximately T(n) with n approximately 2.4+/-0.1, indicating the existence of normal quasiparticles down to at least 0.02T(c). This is in contrast with previous penetration depth measurements on single crystals of NdFeAsO1-xFx and SmFeAsO1-xFx, which indicate an anisotropic but nodeless gap. We discuss possible explanations of the observed power law behavior.

Direct observation of the superconducting gap in phonon spectra

We show that the superconducting energy gap 2Delta can be directly observed in phonon spectra, as predicted by recent theories. In addition, since each phonon probes the gap on only a small part of the Fermi surface, the gap anisotropy can be studied in detail. Our neutron scattering investigation of the anisotropic conventional superconductor YNi2B2C demonstrates this new application of phonon spectroscopy.

Kramer-Pesch approximation for analyzing field-angle-resolved measurements made in unconventional superconductors: a calculation of the zero-energy density of states

By measuring the angular-oscillations behavior of the heat capacity with respect to the applied field direction, one can detect the details of the gap structure. We introduce the Kramer-Pesch approximation as a new method to analyze the field-angle-dependent experiments, which improves the previous Doppler-shift technique. We show that the Fermi-surface anisotropy is an indispensable factor for identifying the superconducting gap symmetry.

Bulk electronic structure of the antiferromagnetic superconducting phase in ErNi2B2C

We have performed temperature- (T-)dependent laser-photoemission spectroscopy of the antiferromagnetic (AF) superconductor ErNi2B2C to study the electronic-structure evolution reflecting the interplay between antiferromagnetism and superconductivity. The spectra at the superconducting (SC) phase show a very broad spectral shape. A T-dependent SC gap shows a sudden deviation from the BCS prediction just below TN. This observation can be explained well by the theoretical model and thus represents the characteristic bulk electronic structure of the AF SC phase for the first time.

Nodal structure of quasi-two-dimensional superconductors probed by a magnetic field

We consider a quasi-two-dimensional superconductor with line nodes in the presence of an in-plane magnetic field, and compute the dependence of the specific heat C and the in-plane heat conductivity kappa on the angle between the field and the nodal direction in the vortex state. We use a variation of the microscopic Brandt-Pesch-Tewordt method that accounts for the scattering of quasiparticles off vortices, and analyze the signature of the nodes in C and kappa. At low to moderate fields the specific heat anisotropy changes sign with increasing temperature. Comparison with measurements of C and kappa in CeCoIn(5) resolves the contradiction between the two in favor of the d((x(2)-y(2)) gap.

Anisotropic diamagnetic response in type-II superconductors with gap and Fermi-surface anisotropies

The effects of anisotropic gap structures on a diamagnetic response are investigated in order to demonstrate that the field-angle-resolved magnetization [ML(chi)] measurement can be used as a spectroscopic method to detect gap structures. Our microscopic calculation based on the quasiclassical Eilenberger formalism reveals that ML(chi) in a superconductor with a fourfold gap displays a fourfold oscillation reflecting the gap and Fermi-surface anisotropies, and the sign of this oscillation changes at a field between Hc1 and Hc2. As a prototype of unconventional superconductors, magnetization data for borocarbides are also discussed.

Evidence of gap anisotropy in superconducting YNi2B2C using directional point-contact spectroscopy

We present a study of the anisotropy in the superconducting energy gap in a single crystal of YNi2B2C (T(c) approximately 14.6 K) using directional point-contact spectroscopy. The superconducting energy gap at 2.7 K, when measured for I||c, is 4.5 times larger than that for I||a. The energy gaps in the two directions also have different temperature dependences. Our results support a scenario with s + g like symmetry.

Evidence for the coexistence of an anisotropic superconducting gap and nonlocal effects in the nonmagnetic superconductor LuNi2B2C

A study of the dependence of the heat capacity C(p)(alpha) on the field angle in LuNi2B2C reveals an anomalous disorder effect. For pure samples, C(p)(alpha) exhibits a fourfold variation as the field H<H(c2) is rotated in the [001] plane, with minima along <100> (alpha=0). A slightly disordered sample, however, develops anomalous secondary minima along <110> for mu(0)H>1 T, leading to an eightfold pattern at 2 K and 1.5 T. The anomalous pattern is discussed in terms of coexisting superconducting gap anisotropy and nonlocal effects.

Anisotropy of the superconducting gap of the borocarbide superconductor YNi2B2C with ultrasonic attenuation

The ultrasonic attenuation alpha of the highly anisotropic s-wave superconductor YNi2B2C has been measured for all the symmetrically independent elastic modes to explore the location of the zero superconducting gap region on the Fermi surface. The attenuation of the longitudinal mode shows a pronounced anisotropy in the superconducting state: While alpha shows a thermally activated behavior along [110] and [001] directions, it shows T-linear dependence along [100]. These results together with those for the transverse modes demonstrate the presence of point nodes or zero-gap regions along [100] and [010] directions. This is a clear demonstration of ultrasonic attenuation as a powerful probe for the structure of the anisotropic superconducting gap.

Evidence for nodal quasiparticles in the nonmagnetic superconductor YNi2B2C via field-angle-dependent heat capacity

Field-angle dependent heat capacity of the nonmagnetic borocarbide superconductor YNi2B2C reveals a clear fourfold oscillation, the first observation of its kind. The observed angular variations were analyzed as a function of magnetic field angle, field-intensity, and temperature to provide its origin. The quantitative agreement between experiment and theory strongly suggests that we are directly observing nodal quasiparticles generated along <100> by the Doppler effect. The results demonstrate that field-angle heat capacity can be a powerful tool in probing the momentum-space gap structure in unconventional superconductors such as high T(c) cuprates, heavy-fermion superconductors, etc.

Multiple superconducting phases in new heavy fermion superconductor PrOs4Sb12

The superconducting gap structure of recently discovered heavy fermion superconductor PrOs4Sb12 was investigated by using thermal transport measurements in magnetic field rotated relative to the crystal axes. We demonstrate that a novel change in the symmetry of the superconducting gap function occurs deep inside the superconducting state, giving a clear indication of the presence of two distinct superconducting phases with twofold and fourfold symmetries. We infer that the gap functions in both phases have a point node singularity, in contrast to the familiar line node singularity observed in almost all unconventional superconductors.

Berry phase in magnetic superconductors

In magnetic systems, electronic bands often acquire nontrivial topological structure characterized by gauge flux distribution in momentum k space. It sometimes follows that the phase of the wave functions cannot be defined uniquely over the whole Brillouin zone. In this Letter, we develop a theory of superconductivity in the presence of this gauge flux both in two- and three-dimensional systems. It is found that the superconducting gap has "nodes" as a function of k where the Fermi surface is penetrated by a gauge string.

Reentrant vortex lattice transformation in fourfold symmetric superconductors

The physics behind the rhombic-->square-->rhombic flux line lattice transformation in increasing fields is clarified on the basis of Eilenberger theory. We demonstrate that this reentrance observed in LuNi2B2C is due to intrinsic competition between the superconducting gap and Fermi surface anisotropies. The calculations not only reproduce it but also predict the not yet found lock-in transition to a square lattice with different orientation in a higher field. In view of the physical origin given, this sequence of transitions is rather generic to occur in fourfold symmetric superconductors.